1. ### Derivative in spherical coordinates

Homework Statement -here is the problem statement -here is a bit of their answer Homework Equations Chain rule, partial derivative in spherical coord. The Attempt at a Solution I tried dragging out the constant and partial derivate with respect to t but still I can't reach their df/dt and...
2. ### A Frechet v Gateaux Derivative and the calculus of variations

Good Morning Could someone please distinguish between the Frechet and Gateaux Derivatives and why one is better to use in the Calculus of Variations? In your response -- if you are so inclined -- please try to avoid the theoretical foundations of this distinction (as I can investigate that by...
3. ### Partial Derivatives

Homework Statement So I know I have to take the derivative with respect to x, then respect to y, then respect to z, but I am not getting the right answer. I know that the answer is 0 and my professor did it with very few steps that I do not understand. Can someone please guide me through it?
4. ### Finding the second derivative using central difference formula

Homework Statement Develop aprogram that will determine the second derivative of pi(16 x^2 - y^4) at y=2 with step sizes of 0.1, 0.01, 0.001…. until the absolute error (numerical-analytical) converges to 0.00001. Use the 2nd order Central Difference Formula. User Input: y, tolerance Output: h...
5. ### I Why do some but not all derivatives have physical meaning?

I know that taking the derivative of certain functions that explain physical phenomena can lead to another statement describing the physical system, the most famous being the derivatives of position. That is, position-->velocity-->acceleration-->jerk-->jounce...and taking any other further...
6. ### Theoretic doubt about the definition of derivatives.

Homework Statement Hi, this is a question that has been bothering me for a while. (Im in calculus II at the moment) Why do i need to derivate some functions by definition and other times i dont? for example if somebody asks me to calculate the partial derivatives of a branch function in a a...
7. ### I A-level differentiation/derivative dilemma

Hello, and thank you for your time. I just started my A-levels derivatives/differentiation , and I would be more than happy if you could help me clarify it. For example I know that y is a function in terms of x right? y=f(x) The derivative of it is f'(x)=dy/dx . This means it is the rate of...

27. ### Is ln(x) differentiable at negative x-axis

Since lnx is defined for positive x only shouldnt the derivative of lnx be 1/x, where x is positive. My books does not specify that x must be positive, so is lnx differentiable for all x?
28. ### Implications of varying the definition of the derivative?

I have been playing around with calculus for a while and I wondered what would it be like to make some changes to the definition of derivatives. I'd like to look at the original definition of derivatives in this way (everything is in lim Δx→0): F(x+Δx) - F(x) = F'(x) * Δx The Δx factor...
29. ### Def. of derivative and cosx=sin(Pi/2-x) to prove y'=-sinx

A lot of web pages/books show how to use cosx=sin(Pi/2-x) and the chain rule to prove that the derivative of cosx=-sinx. My question is how to use this identity and the defintion of the derivative to prove the same thing. Or whether it is at all possible. Seeing that i get...
30. ### Snell's law demonstration?

I can't figure out why my demonstration of snell's law fails, that's the demonstration: (I used a photo) I think it fails because the function t (HO) represents a line and so the concept of minimum is not defined, when I take the derivative and equal it to 0 I'm considering the case when the...